Try to go to places with nursing rooms, bring your pump and cooler bag out. Or if you wanna skip the cooler bag, feed baby the freshly expressed milk. If you intend to pump more than once outside, advised to bring along your own liquid cleanser as 9/10 nursing rooms I went to, the soap bottles are always empty. After that you can dry it with your own tissue/the paper towels provided in the nursing rooms.
I try to limit my time outside ard 3-4hrs max cos I dont want to bring so many things out. Pump right before going out so you have 3hours to not think about pumping. If i will be out longer, will bring along a wearable pump so i can pump with less hassle